Mrs May also pointed to a “steady increase” in Tory membership figures, albeit without referring to numbers, when asked about concerns of entryism in light of Brexiteers from Leave.EU – including Arron Banks – attempting to join to have a say in any leadership election.

On whether she is braced for a leadership challenge from Mr Johnson and her desire to lead the party, Mrs May told reporters: “I’ve been asked before whether it’s my intention to lead the Conservative Party into the next general election, I answered that question before – I’m in this for the long term.

“What I’m focusing on doing is delivering what the British people want – the British people voted for us to leave the European Union and I and the Government will be delivering that.

“But what I’m also focused on doing is delivering on the domestic agenda which is of concern to people.”

Pressed on whether she would fight a leadership challenge from Mr Johnson, the PM replied: “I have said before I am in this for the long term.

Boris Johnson quit the Cabinet over Brexit (Steve Parsons/PA)

“I’m in this for delivering for the British people and that’s what I am focused on.”

Mrs May was also asked if the coup which saw her Oxford University friend Malcolm Turnbull deposed as Australian prime minister reminded her of her fallibility.

The PM said: “I think if you look at Australian politics, they are rather different from the politics we see in the UK.”

On entryism into the Conservatives, Mrs May reiterated that Mr Banks had been unsuccessful in his membership application as he has “actively campaigned against” the party.

Pressed on concerns over potential former Ukip supporters joining or far-right infiltration of Tory Party associations, Mrs May replied: “What we have been doing, we’ve been doing it since the beginning of this year, is working to increase the membership of the party and we’ve seen a steady increase of the membership.”

Looking ahead to October’s party conference, Mrs May said issues to be raised will include housebuilding, technical education and the NHS.

She went on: “There’s a strong domestic agenda that we’ll be taking to our party conference.”